Ok, so first an observation I've made regarding how to serve properly. I've often heard it said that the shoulders should be square with the net at the same time that the arm reaches full extension. The idea is that alignining the timing of the shoulder/chest turn with the timing of the arm extension allows for most efficient power transfer to the ball.

One of the posters here (jollyroger) even posted side by side comparison photos of his serve vs. another poster's serve which illustrated this beautifully.

This makes intuitive sense, however it seems (at least on the face of it) to contradict a principle of whip cracking.

One of the things that allows the kinetic chain to manifest such high speeds is the conservation of angular momentum. Suppose you have three straight pieces of wood, and you connect them together end by end, but allow them to rotate within a certain range of motion. They can rotate 180 degrees in one direction, but once they align up with each other, they cannot rotate any more.

See picture below:

The dashed lines indicate the limits of the "joint angles".

Now suppose the black portion weighs more than the blue portion, and the blue portion weighs more than the red portion.

We can now crack this whip as follows:

We simply rotate the heavy black handle, and then allow the momentum to channel to the next link (the blue one). If the black handle stops moving, all that momentum gets channeled to the blue link. But because the blue link is lighter, it will move faster than the black one did, due to conservation of momentum (mass * velocity). By the time the red one moves independently (due to the black and blue one having reached their joint limits), it's much faster than the original black one.

This principle can be used in cracking the whip of the arm, but my question is whether it should also be used to channel momentum from the torso to the arms.

If so, then wouldn't it make sense to have the shoulders and chest square with the net/target before the arm starts to crack? So long as you prevent the torso from overrotating, and "apply the brakes", then that momentum will be channeled into the arm.

Why doesn't serve instruction encourage this delayed cracking of the whip principle between torso and arms?

According to the paper, and this "whip physics" which does apply to serves by the way, here is what it's trying to really say.

There's a point of giving enough energy where the racket begins to drag itself. This is the part where you're supposed to pronate. By bringing your racket frame vertically, there is very little air friction so it can move faster, right at pronation is when the racket begins to drag itself faster than you can therefore adding a lot of power, while making the racket head flat in order to ensure that you hit the ball.

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Don't you want to "crack the whip" such that the last segment is at max velocity at (close to) full extension? In that case the torso and shoulders will lead the whip earlier in the motion, but all is square right at the cracking.

In one case, the torso reaches squareness by the time at the same time that the arm has fully extended.

In the other case, the torso reaches squareness before the arm starts its whip. The torso remains square while the arm is whipping (so as to channel its angular momentum into the arm), and the arm then fully extends.

think of an open stance forehand where the hips open up to face square to the net/target before the shoulders do. The hips don't overrotate before contact with the ball. That "braking" of the lower, heavier links in the kinetic chain is what this whipping principle is all about. Without the braking, there would be no channeling of momentum up the chain.

Furthermore, in the serve, it only makes sense to talk of squareness with respect to torso alignment relative to net. When the upper arm reaches extension before the forearm does, doesn't really make sense to say that the upper arm becomes square before the forearm does.

Well looking at this clip (http://www.youtube.com/watch?v=vcjZ5r_YHV0), it does seem that the shoulders square with the net before the arm comes around and hits the ball. So cracking of the whip seems to be a good way to describe how energy is channeled from the lower body to the arm and hand.

I don't think it's physiologically feasible for the body to completely stop rotating before each segment of the arm starts to crack. One would develop a very awkward and robotic serve which is contrary to the desirable fluidity in a service motion. With that said, angular momentum should still be still conserved even if the prior segment continues to move. I guess not 100% of the energy would be transfered to to ball in the case where the 2nd to last segment is still rotating upon contact. But I would think a lot more energy is wasted due other imperfections in form.
This concept is used in instructions. I've seen a video from the Serve doctor (Pat Dougherty??) where he actually busted out a whip! Otherwise, instructions such as bending your knees, rotation, racquet head drop all eventually lead to this kinetic chain.

One answer to my question may be that the velocities during the torso-arm link are slow enough that one can engage the chest and shoulder to power the upper arm while piggy backing on the velocity of the twisting torso, rather than use the whip-channeling dynamic.

Yes you're right, it does appear that there is a squaring of the chest prior to shoulder rotation in that federer serve.

I honestly feel that one should strive to develop their own feel for these things. With enough experimentation, one can find their own balance. It's all about developing a feel for exploding into the ball.

you really do not need to have your chest square at the net in order to whip the arm.
undoubtly, the shoulder should stop (or slow down) in order the transfer the kinetic energy to the upper arm.
there is a way to do it, your left hand, instead of drop to the side, drop to the belly buttom, that will create a small brake for the body rotation, the arm then can whip forward easier.

I don't know, I could be way off, but it's been a while now since I've been feeling that the law of conservation of linear/angular momentum is being used improperly to explain stroke mechanics. These laws only apply to a system which is not being acted upon by external forces.

Consider, for example, the open stance forehand of a righty. The right leg is planted on the ground, and the act of pushing off the legs is applying a force on the system of links in the kinetic chain, and this is present through most of the stroke. The core is effectively "pushing" off the hips which is buttressed by the legs planted firmly on the ground. The next kinetic link then pushes of the previous one and so on. There is no conscious or unconscious attempt to stop any of the links for the purpose of transferring momentum to the next link in the chain. IMO, what is really happening is that the "pushing" of one link loads the next one in the sequence, which is then easier to get moving than if it had to start moving without any support from the previous link. This is not momentum transfer.

The same logic applies to serves also. The core and shoulder stop rotating at some point, IMO, because one hits the limits of one's flexibility, not because of any explicit or tacit attempt to transfer momentum.

Anyway, you can see where I am headed with this reasoning. I am, as always, willing to be enlightened gently...

It looks from the original picture that the black portion would have to move downward to get a whip effect.
If you ever 'snapped' a towel, the snapping seems to come moving the towel backward quickly.
Does this seem right?

I don't know, I could be way off, but it's been a while now since I've been feeling that the law of conservation of linear/angular momentum is being used improperly to explain stroke mechanics. These laws only apply to a system which is not being acted upon by external forces.

Consider, for example, the open stance forehand of a righty. The right leg is planted on the ground, and the act of pushing off the legs is applying a force on the system of links in the kinetic chain, and this is present through most of the stroke. The core is effectively "pushing" off the hips which is buttressed by the legs planted firmly on the ground. The next kinetic link then pushes of the previous one and so on. There is no conscious or unconscious attempt to stop any of the links for the purpose of transferring momentum to the next link in the chain. IMO, what is really happening is that the "pushing" of one link loads the next one in the sequence, which is then easier to get moving than if it had to start moving without any support from the previous link. This is not momentum transfer.

The same logic applies to serves also. The core and shoulder stop rotating at some point, IMO, because one hits the limits of one's flexibility, not because of any explicit or tacit attempt to transfer momentum.

Anyway, you can see where I am headed with this reasoning. I am, as always, willing to be enlightened gently...

Thanks for the thoughtful post.

There are certainly many things going on in the "kinetic chain" that facilitate efficient power transfer (and generation). Bear in mind I am by no means an expert. The following thoughts are my own amateur insights.

On the most basic level, you have the "piggyback" effect, where the next link simply goes along for the ride. In this case, it doesn't really function as a new link in the chain, but rather functions as a unit with the previous link.

An example of this would be turning the hips and shoulders together as a single unit, but driving the motion solely through power generated in the muscles that control the hips.

Then you have the conservation of angular momentum effect, which is when a previous and heavier link slows down and as a result transfers the momentum to the higher and lighter set of links. The braking can happen through conscious joint locking, natural joint constraints, or countermovements (for example the role of the left arm in the right handed 1hbh, or the scissor kick where the right leg kicks backwards during the right handed open stance forehand. In both these countermovements, the limb in question prevents the hips from overrotating, allowing better balance and efficient transfer of momentum up to the shoulder and arm).

Then you have independent torque generation at each link. So once the hips stop moving, the upper torso naturally starts to swing, but can be turbo boosted with extra power from the muscles that control the torso swing. This is likely utilized in situations where the velocities and forces are low enough that independent torque generation won't slow things down. In the case of radial deviation of the wrist during the final portion of the serve, a loose wrist facilitates passive torque transfer without any independent power generation that could interfere with the motion. In the case of the link between hips, torso, and shoulder in the 1hbh, I'm almost certain that independent power generation in the abduction of the shoulders can add this turbo boost effect.

Finally you have the stretch reflexes in the muscle, and the natural elasticity of the muscle. This probably comes into play when you have a combination of passive chanelling of momentum as well as active torque generation.

Figuring out which dynamics are at play in which strokes and during which elements of each stroke is a tricky proposal indeed!

True, I believe I may have inadvertently conflated whip physics with the angular momentum channeling principle, simply because I first heard about the principle in that whip physics paper.

That said, I think when it comes to the high velocities involved in service mechanics, the angular momentum principle comes into play especially at the wrist.

There's an interesting thread where this was discussed in quite some depth. I reference one study where a nerve blocking agent was administered to the triceps of throwers. There was little effect upon throwing performance despite this, suggesting a passive role of the elbow joint in throwing.

Here's the thread (I've linked it to a post I made half way through it. The discussion gets interesting towards the end. Brian Gordon, John Yandell, and Dave Smith contribute also).

the consensus seems to be that there is probably complete passivity at the wrist joint, so pure momentum channeling, or what Brian Gordon calls "motion dependent torque". (Gordon remains agnostic on the passivity of the wrist joint due to lack of empirical data that answers the question definitively, but seems to lean towards it, like Yandell, based on observation and experience).